On the Complexity of Finding the Maximum Entropy Compatible Quantum State
Herein we study the problem of recovering a density operator from a set of compatible marginals, motivated by limitations of physical observations. Given that the set of compatible density operators is not singular, we adopt Jaynes’ principle and wish to characterize a compatible density operator wi...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-01-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/9/2/193 |
| _version_ | 1797409731540680704 |
|---|---|
| author | Serena Di Giorgio Paulo Mateus |
| author_facet | Serena Di Giorgio Paulo Mateus |
| author_sort | Serena Di Giorgio |
| collection | DOAJ |
| description | Herein we study the problem of recovering a density operator from a set of compatible marginals, motivated by limitations of physical observations. Given that the set of compatible density operators is not singular, we adopt Jaynes’ principle and wish to characterize a compatible density operator with maximum entropy. We first show that comparing the entropy of compatible density operators is complete for the quantum computational complexity class QSZK, even for the simplest case of 3-chains. Then, we focus on the particular case of quantum Markov chains and trees and establish that for these cases, there exists a procedure polynomial in the number of subsystems that constructs the maximum entropy compatible density operator. Moreover, we extend the Chow–Liu algorithm to the same subclass of quantum states. |
| first_indexed | 2024-03-09T04:18:46Z |
| format | Article |
| id | doaj.art-3052e4dcfaf94ab09277ad32a2093e64 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T04:18:46Z |
| publishDate | 2021-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-3052e4dcfaf94ab09277ad32a2093e642023-12-03T13:49:28ZengMDPI AGMathematics2227-73902021-01-019219310.3390/math9020193On the Complexity of Finding the Maximum Entropy Compatible Quantum StateSerena Di Giorgio0Paulo Mateus1Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, PortugalDepartamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, PortugalHerein we study the problem of recovering a density operator from a set of compatible marginals, motivated by limitations of physical observations. Given that the set of compatible density operators is not singular, we adopt Jaynes’ principle and wish to characterize a compatible density operator with maximum entropy. We first show that comparing the entropy of compatible density operators is complete for the quantum computational complexity class QSZK, even for the simplest case of 3-chains. Then, we focus on the particular case of quantum Markov chains and trees and establish that for these cases, there exists a procedure polynomial in the number of subsystems that constructs the maximum entropy compatible density operator. Moreover, we extend the Chow–Liu algorithm to the same subclass of quantum states.https://www.mdpi.com/2227-7390/9/2/193quantum Markov chainsmaximum von Neumann entropyQSZK-completeness |
| spellingShingle | Serena Di Giorgio Paulo Mateus On the Complexity of Finding the Maximum Entropy Compatible Quantum State Mathematics quantum Markov chains maximum von Neumann entropy QSZK-completeness |
| title | On the Complexity of Finding the Maximum Entropy Compatible Quantum State |
| title_full | On the Complexity of Finding the Maximum Entropy Compatible Quantum State |
| title_fullStr | On the Complexity of Finding the Maximum Entropy Compatible Quantum State |
| title_full_unstemmed | On the Complexity of Finding the Maximum Entropy Compatible Quantum State |
| title_short | On the Complexity of Finding the Maximum Entropy Compatible Quantum State |
| title_sort | on the complexity of finding the maximum entropy compatible quantum state |
| topic | quantum Markov chains maximum von Neumann entropy QSZK-completeness |
| url | https://www.mdpi.com/2227-7390/9/2/193 |
| work_keys_str_mv | AT serenadigiorgio onthecomplexityoffindingthemaximumentropycompatiblequantumstate AT paulomateus onthecomplexityoffindingthemaximumentropycompatiblequantumstate |